Theory of perturbations and analysis of the evolution of quasi-satellite orbits in the restricted three-body problem

Details Theory of perturbations and analysis of the evolution of quasi-satellite orbits in the restricted three-body problem Theory of perturbations and analysis of the evolution of quasi-satellite orbits in the restricted three-body problem

Apr 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993kosis..31...75l&link_type=abstract

Kosmicheskie Issledovaniya (ISSN 0023-4206), vol. 31, no. 2, p. 75-99.

Mathematics

2

Eccentric Orbits, Elliptical Orbits, Perturbation Theory, Satellite Orbits, Three Body Problem, Canonical Forms, Equations Of Motion, Hamiltonian Functions, Lie Groups, Transformations (Mathematics)

Scientific paper

In the restricted elliptic three-body problem, we consider a class of orbits encompassing the body of the smallest mass and located beyond the sphere of its influence. As small parameters we take the ratio of two finite masses, the orbital eccentricity of the body with the smallest mass, the orbit inclination of the zero-mass body (spacecraft), and the ratio of the distance between the zero-mass body and the smallest-mass body to the distance between the finite-mass bodies. By using a series of canonical transformations, the equations of motion are reduced to a form suitable for the application of the Lie method. Evolution equations describing the change of slow variables are obtained up to the third-order terms. Their approximate solution may be used for analyzing the main characteristics of quasi-satellite orbit evolution. Test calculations are carried out for the Mars-Phobos-spacecraft system through the numerical integration of rigorous equations of motion.

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